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Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems


Authors: Moshe Goldberg and Eitan Tadmor
Journal: Math. Comp. 44 (1985), 361-377
MSC: Primary 65M10
DOI: https://doi.org/10.1090/S0025-5718-1985-0777269-7
MathSciNet review: 777269
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Abstract: New convenient stability criteria are provided in this paper for a large class of finite-difference approximations to initial-boundary value problems associated with the hyperbolic system $ {{\mathbf{u}}_t} = A{{\mathbf{u}}_x} + B{\mathbf{u}} + {\mathbf{f}}$ in the quarter plane $ x \geqslant 0$, $ t \geqslant 0$. Using the new criteria, stability is easily established for numerous combinations of well-known basic schemes and boundary conditions, thus generalizing many special cases studied in the recent literature.


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DOI: https://doi.org/10.1090/S0025-5718-1985-0777269-7
Article copyright: © Copyright 1985 American Mathematical Society